14 December 2005

A legendary city was said to have been built on seven islands that were connected to each other and the mainland as follows: Each island had the same number of connections as its rank in size. So, the largest island had 7 connections, the second largest 6, and so on until the smallest island, which had only 1 connection. And the mainland had but one connection to one of the islands.

If the legend is taken literally, explain why no such city could have existed.

The total number of connections, being twice the number of bridges, must be an even number. For example, if there is 1 bridge between 2 islands, each has 1 connection adding up to a total of 2 connections. The total number of connections in the legendary city add up to 29 (7+6+5+4+3+2+1+1). Therefore, the legend is not accurate.